Making a fair choice

[DeGe]

3 friends (A, B, C) want to decide on which restaurant to go to on the weekend. They all have a different preference (Restaurant 1,2, 3).

The only communication between them before the weekend (meeting at the restaurant decided) is through e-mails.

How can they together decide which restaurant to go to in a fair process which involves all 3 of them in the decision making?

[Anza Power]

There are many ways, not sure which one you are looking for.

Let the preference of the friends count as "votes" towards the different restaurants, you pick a restaurant by random where the probabilities are proportional to the number of votes

[OmegaScales]

Would it count if

they agreed to have one of them ask a fourth, random person to choose for them, then tell the others the choice made?

[dgreening]

each person rank orders his choice.

These translate into votes [4 for my first choice, 3 for my second and 1 for my third]

The votes are tallied and the one with the most votes is the choice.

There is still a chance of getting a tie.

So the person ______________ [random variable] will have 3.1 votes for his second choice.

This random variable could be any of the following:

• first to reply
• look at the seconds on the time that the e-mail is posted and the one that is closest to the average of the 3 e-mails,
• the one who's email posting time [last digit only] is closest to the closing DJIE for the day. or
• .....

This approach encourages everyone to think seriously about there 2nd choice.

[phaze]

I think the point is if all 3 are deceitful it gets a little trickier, If person 1 receives an email from person 2 stating that they prefer restaurant A but they do not like this choice they could email person 3 and say "person 1 and myself both want to go to restaurant B"

[DeGe]

they agreed to have one of them ask a fourth, random person to choose for them, then tell the others the choice made?

The fourth person could be influenced by any of the three!

phaze has a valid point regarding answers from Anza and dgreening.

[OmegaScales]

The fourth person could be influenced by any of the three!

How can a random person, whom none of them has ever met, be influenced on such a mundane choice? And don't say money, because it would make no sense to pay someone for such a simple thing.

[phil1882]

they can agree to random chance it.

roll a dice. 1 or 4 equals restaurant 1, 2 or 5; 2; 3 or 6, 3

[harey]

one of them can offer a low amount of money (so that it does not matter who starts). In turn, each one can raise or pass. After two subsequent passes, the last one who raised decides where to go, pays the bill and divides the reminder between the other two.

[Anza Power]

Aha, ok then here's another idea:

First everyone sends everyone their preference, and they all email each other to make sure they have the same information.

Now each one of the three generates a random 1024 bit number, call it x1 x2 x3, but first before revealing those numbers they share a cryprographically secure hash of these numbers (say SHA-512), and then after they make sure everyone know all 3 hashes they share the actual x1 x2 x3, they calculate x1+x2+x3 (mod 2^1024) and treat that as a uniform sampled random number, you can then use it to pick a restaurant

[amateur_reborn]

Persons A and B agree upon (via email) a code to mask the restaurant actual names. For example, X=1, Y=2 and Z=3. This information will not be provided to C.

C will then be asked to pick between X , Y and Z. Once C picks up the value, A and B then reveal what it corresponds to and they all have to go to that restaurant.

[DeGe]

The fourth person could be influenced by any of the three!

How can a random person, whom none of them has ever met, be influenced on such a mundane choice? And don't say money, because it would make no sense to pay someone for such a simple thing.

How will you decide who will choose the "random person" then when the only contact they have is through emails?

they can agree to random chance it.

roll a dice. 1 or 4 equals restaurant 1, 2 or 5; 2; 3 or 6, 3

Who will roll the dice then?

[DeGe]

Persons A and B agree upon (via email) a code to mask the restaurant actual names. For example, X=1, Y=2 and Z=3. This information will not be provided to C.

C will then be asked to pick between X , Y and Z. Once C picks up the value, A and B then reveal what it corresponds to and they all have to go to that restaurant.

What if C thinks that A and B will rig the outcome by changing the restaurant codes once they know the value from C? A possibility if both A and B do not like the restaurant chosen by C?

[DeGe]

Aha, ok then here's another idea:

First everyone sends everyone their preference, and they all email each other to make sure they have the same information.

Now each one of the three generates a random 1024 bit number, call it x1 x2 x3, but first before revealing those numbers they share a cryprographically secure hash of these numbers (say SHA-512), and then after they make sure everyone know all 3 hashes they share the actual x1 x2 x3, they calculate x1+x2+x3 (mod 2^1024) and treat that as a uniform sampled random number, you can then use it to pick a restaurant

Although technically speaking, I don't think there is any flaw in this solution, using this method is way too complicated.

[kukupai]

At first the friends give a number 0, 1 and 2 to the restaurants (for example A=0, B=1, C=2), then they decide an exact time (for example 72 hours before they have to meet ). Now everyone chooses an integer and at this time they send their number to their friends (it has to be done at the exact time to avoid cheating). Once every friend has these three numbers, they add them up and divide the sum by 3. If the remainder is 0, they go to restaurant A, if the remainder is 1, they go to restaurant B, if 2, then the restaurant will be C.

[amateur_reborn]

Persons A and B agree upon (via email) a code to mask the restaurant actual names. For example, X=1, Y=2 and Z=3. This information will not be provided to C.

C will then be asked to pick between X , Y and Z. Once C picks up the value, A and B then reveal what it corresponds to and they all have to go to that restaurant.

What if C thinks that A and B will rig the outcome by changing the restaurant codes once they know the value from C? A possibility if both A and B do not like the restaurant chosen by C?

My assumption was that A, B, C have no preference other than their own favorite restaurant. If C picks up his own favorite restaurant out of X, Y and Z through blind luck (1/3 probability), then A and B have to agree upon a restaurant between A and B's choice to circumvent C's fair selection. They would be each rooting for their own favorite and won't be able to reach a compromise.

In any case, C can always demand a password protected document with the actual translation of X,Y and Z before making the choice. Once C makes the choice, then A or B can reveal the password so that C can open the document and confirm the choice made. Of course, this still leaves the option of C breaking the password if he's a master hacker or something. But I think that would be a stretch and can still be avoided by using a very strong password (encrypting) and asking C to make his choice within a minute of getting the details (so that he won't have time trying to unlock the code). They can all be online to make sure C responds immediately.

Edited August 21, 2013 by amateur_reborn

[phil1882]

who rolls the dice? what difference does that make?

random is random; assuming they aren't professional crap shooters.

if you really insist, they could each roll 1 dice and take the %3 total restaurant.

[phaze]

@Phil Ok, since you rolled a 1, and DeJe rolled a 3, I will say I rolled a 4 or a 1 so we are all going to Porkys Slop Barn

[DeGe]

In any case, C can always demand a password protected document with the actual translation of X,Y and Z before making the choice. Once C makes the choice, then A or B can reveal the password so that C can open the document and confirm the choice made. Of course, this still leaves the option of C breaking the password if he's a master hacker or something. But I think that would be a stretch and can still be avoided by using a very strong password (encrypting) and asking C to make his choice within a minute of getting the details (so that he won't have time trying to unlock the code). They can all be online to make sure C responds immediately.

This is the key point. It prevents any cheating and is fair to all 3.

[kestrelknight]

I just want to say that there are a lot of newbies on the logic puzzle forums. As awesome as that is, I'd just like to mention how lonely we are on the word puzzle forums... Alright, I'm done.